The medical and health care professions have a real and pressing need for a method or means for packaging and preserving biological fluids or fluent components for future use. Much of the prior art teaches freezing biological fluids in a cryogenic medium which is expensive and requires sophisticated handling techniques to avoid a high-loss rate for the cryogenic medium. The prior art also demonstrates a need for maintaining a relatively uniform cross section of the material during the freezing operation to provide uniform and controllable freeze rates across the container to be frozen, and to prevent rupture and damage to cells. In addition, a frozen package of relatively uniform size and cross section greatly simplifies material handling and storage of the biological fluid. Three inch diameter round bottles are widely used at present for human plasma.